In this review, we discuss recent advances in the investigation of colloidal systems interacting via a combination of short-range attraction and long-range repulsion. The prototypical examples of this phenomenology are charged colloids with depletion interactions, but the results apply, to a large extent, also to suspensions of globular proteins, clays, and, in general, to systems with competing attractive (hydrophobic) and repulsive (polar) contributions. After a brief introduction to the problem, we focus on the three disordered states that characterize these systems: equilibrium cluster phase, equilibrium gel, and Wigner glass of clusters. We provide a comparison of their static and dynamic observables, mainly by means of numerical simulations. Next, we discuss the few available studies on their viscoelastic properties and on their response to an external shear. Finally, we provide a summary of the current findings and also raise the main open questions and challenges for the future in this topic.

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